[GAP Forum] Group[HomomorphismByImages
dmitrii.pasechnik at cs.ox.ac.uk
dmitrii.pasechnik at cs.ox.ac.uk
Thu Jul 6 09:54:25 BST 2017
Dear Abdulhakeem,
> Please can someone explain the reason why i am having this error; and a
> possible solution.
> gap> f:=FreeGroup("a","b");
> gap> a:=f.1; b:=f.2;
> gap> rel:=[a^4,b^2,b^-1*a*b*a];
> gap> D8:=f/rel;
> gap> SetReducedMultiplication(D8);
> gap> A:=AutomorphismGroup(D8);
> gap> List(A);
[...]
> gap> f1:=GroupHomomorphismByImages(D8,D8, [ b, b*a^2, a*b ] -> [ b, b*a^2,
> a*b ]);
First of all, a and b are not elements of D8, they are elements of f,
the free group. So you'd first need to do, after defining D8,
a:=D8.1;
b:=D8.2;
(or, perhaps, other variable names, for clarity, etc)
Then, [ b, b*a^2, a*b ] -> [ b, b*a^2, > a*b ] is not valid GAP syntax,
and anyway this is not what GroupHomomorphismByImages expects as input;
instead
f1:=GroupHomomorphismByImages(D8,D8, [ b, b*a^2, a*b ],[ b, b*a^2, a*b ]);
will to the job.
Hope this helps,
Dima
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